Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
6001	35489^4102+4102^35489	128222	Hans Havermann	04/2021
6002	34721^4926+4926^34721	128208	Hans Havermann	04/2021
6003	(305*10^128198+1)/9	128200	Robert Price	02/2020
6004	2^425808-459959	128181	Enzo Doria	06/2015
6005	30632^15291+15291^30632	128178	Hans Havermann	04/2021
6006	U(623603)	128177	Serge Batalov	07/2024
6007	35981^3648+3648^35981	128167	Hans Havermann	04/2021
6008	2^425627-113605	128127	Enzo Doria	08/2014
6009	(4*10^128109+119)/3	128110	Robert Price	12/2021
6010	(22*10^128094+53)/3	128095	Robert Price	07/2019
6011	(86*10^128086-221)/9	128087	Robert Price	09/2019
6012	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
6013	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
6014	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
6015	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
6016	2^425205+4911	128000	Marek Hubal	02/2017
6017	29241^23836+23836^29241	127995	Hans Havermann	04/2021
6018	2^425118-113663	127974	Enzo Doria	08/2014
6019	(86*10^127967-329)/9	127968	Robert Price	01/2020
6020	2^425061+1869761	127957	Enzo Doria	05/2016
6021	746^44541+44541^746	127955	Norbert Schneider	07/2019
6022	30236^17043+17043^30236	127946	Hans Havermann	03/2021
6023	2^424938+212419	127920	Enzo Doria	08/2023
6024	2^424918-21141	127914	Enzo Doria	07/2013
6025	Phi(274823,-3)	127907	Henri Lifchitz	12/2025
6026	(62*10^127903+91)/9	127904	Robert Price	07/2021
6027	2^424864-29489	127897	Enzo Doria	08/2015
6028	30438^15893+15893^30438	127877	Hans Havermann	02/2021
6029	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
6030	28929^26258+26258^28929	127845	Hans Havermann	03/2021
6031	30563^15220+15220^30563	127828	Hans Havermann	03/2021
6032	2^424632-2786639	127827	Enzo Doria	03/2016
6033	10^127821-700001	127821	Robert Price	08/2021
6034	2^424577-113755	127811	Enzo Doria	09/2014
6035	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
6036	(56*10^127752+691)/9	127753	Robert Price	05/2019
6037	11^122629-720	127705	Enzo Doria	11/2012
6038	22*10^127645+3	127647	Robert Price	01/2020
6039	28715^27844+27844^28715	127631	Hans Havermann	03/2021
6040	(56*10^127612+187)/9	127613	Robert Price	10/2021
6041	(5*36^81995+821)/7	127609	Eric Chen	01/2021
6042	4*10^127562-39	127563	Robert Price	09/2020
6043	32595^8186+8186^32595	127547	Hans Havermann	03/2021
6044	2^423696-21429	127546	Enzo Doria	07/2013
6045	2^423664-1864559	127536	Enzo Doria	03/2016
6046	37889^2322+2322^37889	127530	Hans Havermann	03/2021
6047	37668^2429+2429^37668	127523	Hans Havermann	03/2021
6048	3^267267-4	127519	Henri Lifchitz	10/2014
6049	fibonacci(610144)-2	127513	Jon Grantham	08/2023
6050	26253^28852-28852^26253	127503	Frank Doornink	03/2024
6051	(103*10^127491+17)/3	127493	Robert Price	08/2020
6052	29376^21869+21869^29376	127487	Hans Havermann	03/2021
6053	31186^12241+12241^31186	127483	Hans Havermann	02/2021
6054	(19^99689+5^99689)/24	127477	Robert Price	09/2013
6055	7239^33023-7238^33023	127459	Norbert Schneider	02/2026
6056	27069^28754-28754^27069	127452	Frank Doornink	01/2024
6057	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
6058	30594^14645+14645^30594	127446	Hans Havermann	03/2021
6059	2^423328-21537	127435	Enzo Doria	07/2013
6060	(67*10^127413-7)/3	127415	Robert Price	01/2020
6061	(5*34^83193+700233)/11	127408	Eric Chen	08/2023
6062	(2*10^127407+73)/3	127407	Robert Price	09/2020
6063	(2^423165-7)/25	127384	Lelio R Paula	05/2015
6064	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
6065	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
6066	29512^20647+20647^29512	127341	Hans Havermann	03/2021
6067	2^422987-3001935	127332	Paul Bourdelais	07/2023
6068	(112*10^127324+17)/3	127326	Robert Price	03/2020
6070	29565^20252+20252^29565	127321	Hans Havermann	03/2021
6069	232^232^232+1831^1831	127321	Henri Lifchitz	03/2025
6071	fibonacci(609165)-3	127308	Jon Grantham	08/2023
6073	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
6072	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
6074	(16*10^127259+197)/3	127260	Robert Price	04/2019
6075	(26*10^127240+61)/3	127241	Robert Price	10/2019
6076	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
6077	2^422515-114997	127190	Enzo Doria	06/2015
6078	5*10^127179-3	127180	Robert Price	07/2015
6079	31678^10343+10343^31678	127176	Hans Havermann	03/2021
6080	(44*10^127169-233)/9	127170	Robert Price	01/2019
6081	34947^4352+4352^34947	127162	Hans Havermann	03/2021
6082	6*10^127158+19	127159	Robert Price	11/2021
6083	30469^14902+14902^30469	127155	Hans Havermann	03/2021
6084	5*10^127153+77	127154	Robert Price	12/2018
6085	29941^17620+17620^29941	127130	Hans Havermann	02/2021
6086	31607^10516+10516^31607	127119	Hans Havermann	03/2021
6087	(19*10^127118-97)/3	127119	Robert Price	10/2021
6088	(29*10^127111+691)/9	127112	Robert Price	08/2021
6089	736^44335+44335^736	127104	Norbert Schneider	07/2019
6090	33040^7023+7023^33040	127090	Hans Havermann	03/2021
6091	(4*10^127081+167)/9	127081	Robert Price	03/2022
6092	29748^18661+18661^29748	127052	Hans Havermann	03/2021
6093	27905^28578-28578^27905	127049	Frank Doornink	03/2024
6094	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
6095	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
6096	(49^75161+3^75161)/52	127036	Robert Price	07/2026
6097	(14*10^127014-137)/3	127015	Robert Price	04/2021
6098	31436^10965+10965^31436	127002	Hans Havermann	03/2021
6099	28905^24758+24758^28905	127001	Hans Havermann	03/2021
6100	2^421860-113285	126993	Enzo Doria	07/2014
6101	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
6102	(2^421827-7)/11	126982	Lelio R Paula	05/2015
6103	26268^28729-28729^26268	126966	Frank Doornink	03/2024
6104	11^121910-840	126957	Enzo Doria	12/2012
6105	(56*10^126935+187)/9	126936	Robert Price	10/2021
6106	28915^24538+24538^28915	126933	Hans Havermann	03/2021
6107	(29*10^126928-77)/3	126929	Robert Price	02/2020
6108	(259*10^126919-1)/3	126921	Robert Price	12/2020
6109	10^126919+204567	126920	Patrick De Geest	05/2021
6110	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
6111	10^126919-100001	126919	Robert Price	07/2020
6112	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
6113	2^421534-3001935	126895	Paul Bourdelais	07/2023
6114	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
6115	(5*10^126871-119)/3	126872	Robert Price	03/2018
6116	Phi(47471,561)	126871	Henri Lifchitz	12/2025
6117	331^50339-10004	126846	Enzo Doria	07/2012
6118	2^421363-2790757	126843	Enzo Doria	03/2016
6119	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
6120	37938^2203+2203^37938	126828	Hans Havermann	03/2021
6121	(13*10^126819+77)/9	126820	Robert Price	07/2022
6122	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
6124	(14*10^126784-83)/3	126785	Robert Price	12/2018
6123	2^421169-3001935	126785	Paul Bourdelais	07/2023
6125	2^421161-286183	126783	Enzo Doria	06/2015
6126	26733^28628-28628^26733	126738	Frank Doornink	03/2024
6127	(106*10^126726+17)/3	126728	Robert Price	04/2021
6128	30718^13347+13347^30718	126724	Hans Havermann	03/2021
6129	2^420939-113935	126716	Enzo Doria	10/2014
6130	11*23^93048+356	126708	Eric Chen	08/2023
6131	177^56363-2	126703	Lelio R Paula	10/2017
6132	2^420741-113659	126656	Enzo Doria	08/2014
6133	2^420694-21	126642	Lelio R Paula	05/2017
6134	(28^87511+5^87511)/33	126641	Robert Price	09/2026
6136	(13*10^126638+437)/9	126639	Robert Price	04/2018
6135	(167*10^126637-17)/3	126639	Robert Price	03/2020
6137	4*10^126625+87	126626	Robert Price	08/2018
6138	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
6139	7*10^126600-99	126601	Robert Price	06/2019
6140	U(655247)/250330563881/206066063082749	126596	Serge Batalov	07/2024
6141	2^420424-59189	126561	Enzo Doria	10/2015
6142	28717^25534+25534^28717	126560	Hans Havermann	03/2021
6143	(86*10^126542+103)/9	126543	Robert Price	12/2021
6144	(19*10^126517-7)/3	126518	Robert Price	12/2023
6145	2026^38261-2025^38261	126516	Henri Lifchitz	12/2025
6146	28922^23655+23655^28922	126503	Hans Havermann	03/2021
6147	2^420126+71893	126471	Enzo Doria	04/2016
6148	25982^28643-28643^25982	126450	Frank Doornink	03/2024
6149	(43*10^126441+47)/9	126442	Robert Price	12/2018
6150	8*10^126408+71	126409	Robert Price	05/2022
6151	2^419866+1877059	126393	Enzo Doria	07/2016
6152	29315^20484+20484^29315	126390	Hans Havermann	03/2021
6153	29433^19676+19676^29433	126384	Hans Havermann	03/2021
6154	F(604711)	126377	Henri Lifchitz	02/2005
6155	2^419757+72707	126360	Enzo Doria	04/2016
6156	2^419720-21569	126349	Enzo Doria	07/2013
6157	2^419637+29	126324	Henri Lifchitz	02/2006
6158	31004^11865+11865^31004	126319	Hans Havermann	03/2021
6159	2^419612+1876741	126316	Enzo Doria	07/2016
6160	2^419520+2793271	126289	Enzo Doria	03/2016
6161	(2^419447-5)/369	126264	Lelio R Paula	05/2014
6162	2^419328-1859939	126231	Enzo Doria	03/2016
6163	2^419282-1851507	126217	Enzo Doria	08/2015
6164	(133*10^126212+17)/3	126214	Robert Price	11/2021
6165	2^419251+1866143	126208	Enzo Doria	03/2016
6166	11^121185+2	126202	Robert Price	05/2014
6167	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
6168	Phi(267889,3)	126161	Henri Lifchitz	12/2025
6169	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
6170	2^418851+23	126087	Robert Price	09/2015
6171	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
6172	2^418829+167	126081	Lelio R Paula	01/2012
6173	31037^11530+11530^31037	126067	Hans Havermann	03/2021
6174	4*10^126064-69	126065	Robert Price	01/2022
6175	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
6176	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
6177	(35*10^126048-323)/9	126049	Robert Price	10/2021
6178	33016^6551+6551^33016	126000	Hans Havermann	03/2021
6179	2^418548-111546435	125996	Paul Bourdelais	10/2021
6180	2^418466-305741	125971	Maxim Gerspach	08/2026
6181	25134^28625-28625^25134	125958	Frank Doornink	12/2023
6182	34736^4227+4227^34736	125954	Hans Havermann	03/2021
6183	(23*35^81566-144013)/34	125944	Eric Chen	05/2025
6184	26197^28502-28502^26197	125930	Frank Doornink	03/2024
6185	2^418319-109501	125927	Enzo Doria	04/2014
6186	2^418316-112373	125926	Enzo Doria	06/2014
6187	40398^1309+1309^40398	125919	Hans Havermann	03/2021
6188	997^41985+996	125901	Alfred Reich	03/2026
6189	(8*10^125894-29)/3	125895	Robert Price	07/2018
6190	(26*10^125886-413)/9	125887	Robert Price	05/2018
6191	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
6192	55*10^125847+9	125849	Robert Price	03/2022
6193	4*10^125832+57	125833	Robert Price	05/2022
6194	2^417968+1869811	125821	Enzo Doria	06/2016
6195	2^417902+63	125802	Lelio R Paula	09/2015
6196	(10^125792-91)/9	125792	Serge Batalov	12/2014
6197	30438^13573+13573^30438	125791	Hans Havermann	03/2021
6198	32867^6714+6714^32867	125782	Hans Havermann	03/2021
6199	31155^10892+10892^31155	125777	Hans Havermann	03/2021
6200	(35*10^125754-593)/9	125755	Robert Price	07/2018
6201	30455^13464+13464^30455	125754	Hans Havermann	03/2021
6202	(32*10^125751-77)/9	125752	Robert Price	06/2018
6203	2^417704+77011	125742	Enzo Doria	05/2016
6204	29755^16816+16816^29755	125737	Hans Havermann	03/2021
6205	(22*10^125734+203)/9	125735	Robert Price	10/2021
6206	29918^15915+15915^29918	125710	Hans Havermann	03/2021
6207	(10^125706+149)/3	125706	Serge Batalov	12/2014
6208	28531^25368+25368^28531	125659	Hans Havermann	03/2021
6209	2^417419-115309	125656	Enzo Doria	07/2015
6210	(46*10^125642+593)/9	125643	Robert Price	04/2022
6211	2^417315+213953	125625	Enzo Doria	10/2023
6212	2^417300+77281	125620	Enzo Doria	05/2016
6213	30638^12537+12537^30638	125561	Hans Havermann	03/2021
6214	2^417095-1657	125559	Yves Minet	07/2014
6215	30162^14525+14525^30162	125538	Hans Havermann	03/2021
6216	(56*10^125535+583)/9	125536	Robert Price	08/2021
6217	(23*10^125517-179)/3	125518	Robert Price	06/2022
6218	9*10^125516+29	125517	Robert Price	03/2022
6219	404*35^81280+23	125505	Eric Chen	05/2025
6220	(88*10^125492-637)/9	125493	Robert Price	11/2020
6221	28958^21525+21525^28958	125474	Hans Havermann	02/2021
6224	2^416773-25	125462	Lelio R Paula	09/2015
6222	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
6223	26078^28409-28409^26078	125462	Frank Doornink	03/2024
6225	33889^5032+5032^33889	125449	Hans Havermann	03/2021
6226	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
6227	(2861^36481+1)/(2861^191+1)	125438	Martin Hopf	12/2023
6228	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
6229	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
6230	2^416641-2*416641+1	125422	Robert Price	05/2018
6231	33392^5697+5697^33392	125409	Hans Havermann	03/2021
6232	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
6233	2^416530+1870429	125389	Enzo Doria	05/2016
6234	(56*10^125385+691)/9	125386	Robert Price	05/2019
6235	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
6236	31074^10837+10837^31074	125381	Hans Havermann	03/2021
6237	33745^5194+5194^33745	125380	Hans Havermann	03/2021
6238	2^416490+1875109	125376	Enzo Doria	09/2016
6239	28360^26331+26331^28360	125365	Hans Havermann	03/2021
6240	2^416416-114929	125354	Enzo Doria	05/2015
6241	25805^28412-28412^25805	125346	Frank Doornink	03/2024
6242	(77*10^125330-293)/9	125331	Robert Price	09/2019
6243	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
6244	2^416134+1865899	125269	Enzo Doria	03/2016
6245	153^57337-152	125264	Norbert Schneider	12/2018
6246	(599*10^125224+13)/9	125226	Robert Price	02/2022
6247	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
6248	30054^14657+14657^30054	125207	Hans Havermann	03/2021
6249	(23^91943-1)/22	125201	Robert Price	01/2012
6250	2^415884-933075	125194	Paul Bourdelais	06/2021

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Probable Primes Top 10000

(303416 PRPs in the top)